Sir Alex Ferguson's side had gone 27 league matches without losing, a run stretching back to their 2-1 defeat against Chelsea in April last season.
But that sequence looked in danger as goals from former United defender Craig Cathcart and striker DJ Campbell put the Seasiders 2-0 up at half-time.
Blackpool could have had a penalty when Luke Varney was bundled over by Rafael da Silva early in the second half.
But United finally got one back when in-form Bulgarian forward Dimitar Berbatov volleyed home Darren Fletcher's cross in the 72nd minute.
Mexican striker Javier Hernandez, on for the lacklustre Wayne Rooney, equalised when he ran onto a Ryan Giggs pass and slotted past Richard Kingson in the 74th minute.
United right-back Rafael was carried off on a stretcher after lengthy treatment on a head injury, but Berbatov stole the points in the 88th minute as he drove beyond Kingson to leave the leaders well ahead of second placed Arsenal.
In Tuesday's other Premier League clash, Aston Villa won 2-1 at third bottom Wigan to move six points away from the relegation zone.
Gabriel Agbonlahor opened the scoring in the 49th minute when he nodded home after Ali Al Habsi saved Carlos Cuellar's header.
Gerard Houllier's side, who beat Manchester City on Saturday, wrapped up the points in the 62nd minute when Ashley Young converted a penalty after being fouled by Hendry Thomas.
James McCarthy's deflected effort reduced the deficit in the 80th minute but it was too late for Wigan to salvage a draw.